Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40501	Find Trig Functions Using Identities	cos(pi/2-theta)	$\cos (\frac{π}{2} - θ)$
40502	Convert to Rectangular Coordinates	(-3,120 degrees )	$(- 3, 120 °)$
40503	Convert to Rectangular Coordinates	(-3,pi)	$(- 3, π)$
40504	Convert to Interval Notation	(2x+3)/(x^2+2x-15)>=0	$\frac{2 x + 3}{x^{2} + 2 x - 15} \geq 0$
40505	Convert to Interval Notation	(x-5)/(x+3)>=0	$\frac{x - 5}{x + 3} \geq 0$
40506	Factor	16x^2-36x^4	$16 x^{2} - 36 x^{4}$
40507	Factor	4x^4-45x^2+81	$4 x^{4} - 45 x^{2} + 81$
40508	Find Amplitude, Period, and Phase Shift	y=-1/3sin(2x)	$y = - \frac{1}{3} \sin (2 x)$
40509	Find Amplitude, Period, and Phase Shift	y=-3cos(1/4x)	$y = - 3 \cos (\frac{1}{4} x)$
40510	Find the x and y Intercepts	y=tan(x-pi/6)	$y = \tan (x - \frac{π}{6})$
40511	Find the x and y Intercepts	y=tan(x+pi/3)	$y = \tan (x + \frac{π}{3})$
40512	Find the Asymptotes	f(x)=(5x^2)/(x^2-1)	$f (x) = \frac{5 x^{2}}{x^{2} - 1}$
40513	Find the Domain	g(x)=(3x)/(x^2-81)	$g (x) = \frac{3 x}{x^{2} - 81}$
40514	Expand the Logarithmic Expression	log base 7 of ( square root of 7x^9)/y	$\log_{7} (\frac{\sqrt{7 x^{9}}}{y})$
40515	Find the Value Using the Unit Circle	-(3pi)/4	$- \frac{3 π}{4}$
40516	Find the Domain	( square root of x-5)^2	${(\sqrt{x - 5})}^{2}$
40517	Convert to Logarithmic Form	square root of 9=3	$\sqrt{9} = 3$
40518	Use the Rational Roots Test to Find All Possible Roots	f(x)=5x^3+28x^2+16x+5	$f (x) = 5 x^{3} + 28 x^{2} + 16 x + 5$
40519	Convert to Rectangular	rsin(theta)=4	$r \sin (θ) = 4$
40520	Divide	(2pi)/(1/5)	$\frac{2 π}{\frac{1}{5}}$
40521	Divide	pi/(1/2)	$\frac{π}{\frac{1}{2}}$
40522	Find the Trig Value	sin(theta)=5/13	$\sin (θ) = \frac{5}{13}$
40523	Find Trig Functions Using Identities	(sin(theta))/(cos(theta))+(cos(theta))/(sin(theta))	$\frac{\sin (θ)}{\cos (θ)} + \frac{\cos (θ)}{\sin (θ)}$
40524	Convert from Degrees to Radians	-690 degrees	$- 690 °$
40525	Complete the Square	x^2-6x-11	$x^{2} - 6 x - 11$
40526	Convert to Interval Notation	(2x+3)/(x^2+4x-21)>=0	$\frac{2 x + 3}{x^{2} + 4 x - 21} \geq 0$
40527	Convert to Interval Notation	x^3-3x^2-x+3>=0	$x^{3} - 3 x^{2} - x + 3 \geq 0$
40528	Convert to Interval Notation	(3-x)^2(x-9/2)<0	${(3 - x)}^{2} (x - \frac{9}{2}) < 0$
40529	Find the Asymptotes	f(x)=(x^2-100)/(x-10)	$f (x) = \frac{x^{2} - 100}{x - 10}$
40530	Find All Complex Solutions	sin(x)=-( square root of 3)/2	$\sin (x) = - \frac{\sqrt{3}}{2}$
40531	Convert to Logarithmic Form	fourth root of 625=5	$\sqrt[4]{625} = 5$
40532	Find the Asymptotes	(x^2+x-12)/(x-4)	$\frac{x^{2} + x - 12}{x - 4}$
40533	Find the Inverse	y=cos(x-pi/2)	$y = \cos (x - \frac{π}{2})$
40534	Find the Value Using the Unit Circle	(7pi)/6	$\frac{7 π}{6}$
40535	Find the Roots (Zeros)	x^5-x^4-5x^3+x^2+8x+4	$x^{5} - x^{4} - 5 x^{3} + x^{2} + 8 x + 4$
40536	Find the Roots (Zeros)	2x^3+3x^2-1	$2 x^{3} + 3 x^{2} - 1$
40537	Find the Inverse	f^-1(6)	$f^{- 1} (6)$
40538	Convert to Rectangular	5/2(cos(150 degrees )+isin(150 degrees ))	$\frac{5}{2} (\cos (150 °) + i \sin (150 °))$
40539	Convert to Rectangular	square root of 6(cos(315 degrees )+isin(315 degrees ))	$\sqrt{6} (\cos (315 °) + i \sin (315 °))$
40540	Divide	180/pi	$\frac{180}{π}$
40541	Divide	37/2	$\frac{37}{2}$
40542	Multiply	165*2	$165 \cdot 2$
40543	Find the Trig Value	sin(3theta)=-1	$\sin (3 θ) = - 1$
40544	Find the Vertex	y=-x^2-8x-16	$y = - x^{2} - 8 x - 16$
40545	Convert to Rectangular Coordinates	(-3,-135 degrees )	$(- 3, - 135 °)$
40546	Convert to Rectangular Coordinates	(2,3pi)	$(2, 3 π)$
40547	Factor	csc(x)^2-1	$\csc^{2} (x) - 1$
40548	Factor	6x^2-34x+20	$6 x^{2} - 34 x + 20$
40549	Find the x and y Intercepts	y=tan(x+pi/4)	$y = \tan (x + \frac{π}{4})$
40550	Find the x and y Intercepts	y=tan(x+pi/6)	$y = \tan (x + \frac{π}{6})$
40551	Verify the Identity	cot(theta)*sec(theta)=csc(theta)	$\cot (θ) \cdot \sec (θ) = \csc (θ)$
40552	Verify the Identity	cos(theta)*csc(theta)=cot(theta)	$\cos (θ) \cdot \csc (θ) = \cot (θ)$
40553	Factor over the Complex Numbers	sin(arcsec(u))	$\sin (arcsec (u))$
40554	Convert to Interval Notation	x^3-4x<=0	$x^{3} - 4 x \leq 0$
40555	Convert to Interval Notation	((x+10)(x-12))/(x+8)<=0	$\frac{(x + 10) (x - 12)}{x + 8} \leq 0$
40556	Convert to Interval Notation	(x-8)(x+9)(7x+9)<0	$(x - 8) (x + 9) (7 x + 9) < 0$
40557	Verify the Identity	sin(theta)*sec(theta)=tan(theta)	$\sin (θ) \cdot \sec (θ) = \tan (θ)$
40558	Find the Vertex	f(x)=x^2-10x+24	$f (x) = x^{2} - 10 x + 24$
40559	Find the Asymptotes	(x+5)/(x^2-25)	$\frac{x + 5}{x^{2} - 25}$
40560	Find the Asymptotes	(x^2+1)/(x^3+2)	$\frac{x^{2} + 1}{x^{3} + 2}$
40561	Find the Roots (Zeros)	f(x)=x^3-13x^2+59x-87	$f (x) = x^{3} - 13 x^{2} + 59 x - 87$
40562	Find the Roots (Zeros)	2x^6-3x^5-13x^4+29x^3-27x^2+32x-12	$2 x^{6} - 3 x^{5} - 13 x^{4} + 29 x^{3} - 27 x^{2} + 32 x - 12$
40563	Find the Roots (Zeros)	-x^3+4x^2+15x-18	$- x^{3} + 4 x^{2} + 15 x - 18$
40564	Find the Inverse	y=pi/4+sin(x)	$y = \frac{π}{4} + \sin (x)$
40565	Find the Asymptotes	f(x)=(x^3)/(x^2-1)	$f (x) = \frac{x^{3}}{x^{2} - 1}$
40566	Divide	360/3	$\frac{360}{3}$
40567	Divide	1/(5/13)	$\frac{1}{\frac{5}{13}}$
40568	Find the Trig Value	sin(theta)=-3/5	$\sin (θ) = - \frac{3}{5}$
40569	Find the Trig Value	cos(2theta)	$\cos (2 θ)$
40570	Convert to Rectangular Coordinates	(4,315 degrees )	$(4, 315 °)$
40571	Verify the Identity	(csc(theta)+cot(theta))(csc(theta)-cot(theta))=1	$(\csc (θ) + \cot (θ)) (\csc (θ) - \cot (θ)) = 1$
40572	Convert to Interval Notation	x^3-144x<=0	$x^{3} - 144 x \leq 0$
40573	Convert to Interval Notation	x^3-81x<=0	$x^{3} - 81 x \leq 0$
40574	Find All Complex Solutions	2sin(x)^2=sin(x)	$2 \sin^{2} (x) = \sin (x)$
40575	Find the Range	arcsin(x)	$\arcsin (x)$
40576	Find the Domain and Range	y=2\|cos(x)\|-1	$y = 2 \| \cos (x) \| - 1$
40577	Find the Asymptotes	((x+1)(x-1))/((3x+5)(x+2))	$\frac{(x + 1) (x - 1)}{(3 x + 5) (x + 2)}$
40578	Find the Roots/Zeros Using the Rational Roots Test	f(x)=7x^3+53x^2+29x+7	$f (x) = 7 x^{3} + 53 x^{2} + 29 x + 7$
40579	Find the Roots (Zeros)	2x^5-29x^4+112x^3-74x^2+350x-1225	$2 x^{5} - 29 x^{4} + 112 x^{3} - 74 x^{2} + 350 x - 1225$
40580	Find the Range	f(x)=-3sin(x/2-pi/3)+5	$f (x) = - 3 \sin (\frac{x}{2} - \frac{π}{3}) + 5$
40581	Find the Value Using the Unit Circle	cos(270 degrees )	$\cos (270 °)$
40582	Convert Degrees, Minutes, Seconds to Decimal Degrees	12 degrees 12'12''	$12 ° 12' 12''$
40583	Find the Inverse	cube root of x-7	$\sqrt[3]{x - 7}$
40584	Find Amplitude, Period, and Phase Shift	y=3sin(2x-2pi)	$y = 3 \sin (2 x - 2 π)$
40585	Find Amplitude, Period, and Phase Shift	y=3sin(5x)	$y = 3 \sin (5 x)$
40586	Find the Asymptotes	f(x)=(x^2-144)/(x-12)	$f (x) = \frac{x^{2} - 144}{x - 12}$
40587	Find the Asymptotes	f(x)=(x^2+4x-12)/(x-6)	$f (x) = \frac{x^{2} + 4 x - 12}{x - 6}$
40588	Divide	(2pi)/8	$\frac{2 π}{8}$
40589	Find the Vertex	f(x)=-1/2x^2-4x+10	$f (x) = - \frac{1}{2} x^{2} - 4 x + 10$
40590	Convert to Interval Notation	x^2-8x+16<=0	$x^{2} - 8 x + 16 \leq 0$
40591	Find the Inverse	[[7,12],[-8,-5]]	$[\begin{array}{c} 7 & 12 \\ - 8 & - 5 \end{array}]$
40592	Factor	(sin(theta)+cos(theta))^2+(sin(theta)-cos(theta))^2	${(\sin (θ) + \cos (θ))}^{2} + {(\sin (θ) - \cos (θ))}^{2}$
40593	Factor	15x^2+52x+45	$15 x^{2} + 52 x + 45$
40594	Find the Degree	sec(theta) = square root of 2	$\sec (θ) = \sqrt{2}$
40595	Find the Third Derivative	y=4x^6+3x^5-7x^3-5x^2+11	$y = 4 x^{6} + 3 x^{5} - 7 x^{3} - 5 x^{2} + 11$
40596	Find the Reciprocal	pi/6	$\frac{π}{6}$
40597	Add	(sin(theta))/(cos(theta))+(cos(theta))/(sin(theta))	$\frac{\sin (θ)}{\cos (θ)} + \frac{\cos (θ)}{\sin (θ)}$
40598	Find the Roots (Zeros)	f(x)=7x^3+53x^2+29x+7	$f (x) = 7 x^{3} + 53 x^{2} + 29 x + 7$
40599	Find the Domain and Range	y=tan(pi/5x)	$y = \tan (\frac{π}{5} x)$
40600	Find the Roots (Zeros)	16x^4-72x^3+113x^2-44x+5	$16 x^{4} - 72 x^{3} + 113 x^{2} - 44 x + 5$